ergodic theory
"Ergodic theory" is a branch of mathematics focused on understanding the long-term behavior of dynamical systems.
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Definition
C2Mathematics
(technical, academic)The study of statistical properties and long-term behavior of dynamical systems.
Example
- Ergodic theory helps mathematicians understand how a system evolves over time.
- Research in ergodic theory has applications in fields like physics and economics.
C2Statistical Physics
(technical, academic)Examines the conditions under which time averages of a system's observables match space averages.
Example
- In statistical physics, ergodic theory is used to explain thermodynamic behavior.
- The principles of ergodic theory are fundamental to understanding equilibrium in physical systems.